BAGHDAD, Iraq (CNN) -- Shiite militias fought U.S. and Iraqi forces in Sadr City, Baghdad, for a seventh day Saturday and a vehicle ban continued to frustrate residents, driven indoors for a week by the battles.

Iraqi boys set fire Saturday to an Iraqi army vehicle destroyed earlier in Baghdad's Sadr City enclave.

Rocket or mortar fire also struck the Green Zone, the heavily secured neighborhood that is the U.S. seat of power, but no casualities were reported, the U.S. Embassy said.

The U.S.-backed Iraqi troops are fighting the Mehdi Army militia -- which is loyal to Shiite cleric Muqtada al-Sadr -- in the sprawling, crowded Baghdad slum.

Witnesses said U.S. aircraft bombarded the area for hours, while media reported rockets slamming into houses and many casualties.

Authorities had planned to lift the vehicle ban in Baghdad at 6 a.m. Saturday amid concerns that the curfew was causing a humanitarian crisis, but residents complain the strictures are still in place.

Iraq's Interior Ministry, however, said the ban has been lifted in some areas, and witnesses said a vehicle entry point into Sadr City has been opened.

Witnesses and al-Sadr's office said loudspeaker announcements broadcast from mosques offered updates about Mehdi Army attacks on U.S. military vehicles.

The U.S. military said no U.S. or Iraqi troops were seriously hurt in the fighting. However, a U.S. soldier was killed Saturday by a roadside bomb elsewhere in Baghdad, the military said.

Authorities warned Sadr City residents to be careful if they ventured into the streets.

"Outlaw groups have planted roadside bombs and other explosives in most of the streets of Sadr City and for the safety of our people and journalists we urge they stay away from restricted roads for the time being and until they are cleared by security forces," the Baghdad Operations Command said on its Web site Saturday.

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Sadr City is one of several Iraqi areas gripped by intra-Shiite fighting that erupted March 25, when Iraqi security forces began a crackdown on criminal elements in the southern city of Basra, a mostly Shiite city.

The fighting spread to other Shiite cities in the south and then to the Shiite neighborhoods of Baghdad, leaving hundreds dead.

The fighting intensified in Sadr City after the killing Friday of one of al-Sadr's top aides in the Shiite holy city of Najaf. Al-Sadr said Sayyed Riyadh al-Nuri was shot outside his house after returning from Friday prayers.

Al-Sadr called for calm and demanded a government investigation and arrests of those responsible. And he called on all political and religious groups to try to end the targeting of religious symbols and groups and religion students.

Separately Saturday, the U.S. military raised the number of bodies found at a house just south of Baghdad to 45.

Iraqi soldiers found the mass grave in Mahmoudiya on Thursday, and military authorities believe the bodies have been there for more than a year.

Troops -- who initially found 33 bodies -- have been excavating the site since it was discovered.E-mail to a friend